Molecular spin-orbit constants

A semiempirical calculation of molecular spin-orbit constants can be made, using the method of Ishiguro and Kobori (1967). 

Calculated and experimental states of LaO. State energies are given incm . The molecular spin-orbit constant A is defined by the relation < AAS. Reproduced from Kotzian et al. (1991a). 

A or Av - fine structure or molecular spin orbit coupling constant for vibration level v. Equation (7.187). 

Klisch, Belov, Schieder, Winnewisser and Herbst [157] have combined all of the data for NO to produce a current best set of molecular constants for three isotopomers, presented in table 10.15. The data used, apart from their own terahertz studies, included the A-doubling of Meerts and Dymanus [156, 158], the sub-millimetre transitions of 15N160 and 14NlsO, and Fourier transform data from Salek, Winnewisser and Yamada [159]. These last authors were able to study the magnetic dipole transitions between the two fine-structure states. The values of the spin orbit constant A for the less common isotopomers come from Amiot, Bacis and Guelachvih [160]. 

The difference between the spin-orbit constants of the main constituent atomic orbital, A(atom, nl), in the Rydberg molecular orbital and that of the molecular Rydberg state, Ar, is due to penetration of the Rydberg MO into the molecular core, i.e., to the contribution of the (n — l) atomic orbital responsible for the orthogonality between the Rydberg MO and the molecular core orbitals. 

In Section 3.4.2, spin-orbit matrix elements are expressed, in the single-configuratioi approximation, in terms of molecular spin-orbit parameters. These molecular parameters can also be related to atomic spin-orbit parameters. In Table 5.6, some values are given for atomic spin-orbit constants, (nl). Sections 5.3.1 and... 

For heteronuclear molecules, ab initio calculations of the Self-Consistent-Field (SCF) molecular orbitals are usually necessary to obtain the values of the Ck coefficients. The values of the spin-orbit constants depend on the effective charge on each atom, a positive charge causing a contraction of the atomic orbitals and an increase in C(atomic) a negative charge causes an opposite effect. In the simple case of an expansion of the molecular orbitals in terms of a large number of atomic orbitals associated with a single 1-value on each atom (Lefebvre-Brion and Moser, 1966),... 

This result may be extended to the case of a molecular orbital expanded in terms of many atomic orbitals similarly to that for diagonal spin-orbit constants... 

In the case of SeH, it was the first time molecular fine structure was measured by photodetachment 235). jwo thresholds assigned to transitions from SeH ( S+) to the two final states 2II3/2 and 2IIi/2leadtoa determination of the molecular spin-orbit coupling constant A(SeH ) = -1815 100 cm-i. 

To avoid having the wave function zero everywhere (an unacceptable solution), the spin orbitals must be fundamentally different from one another. Eor example, they cannot be related by a constant factor. You can write each spin orbital as a product of a space function which depends only on the x, y, and z coordinates of the electron—and a spin function. The space function isusually called the molecular orbital. While an infinite number of space functions are possible, only two spin functions are possible alpha and beta. 

Pople, J. A., Santry, D. P. . Molecular Orbital Theory of Nuclear Spin Coupling Constants. Mol. Phys. 8, 1 (1964). 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

We should note that if g = ge, the contact shift is isotropic (independent of orientation). If g is different from ge and anisotropic (see Section 1.4), then the contact shift is also anisotropic. The anisotropy of the shift is due to the fact that (1) the energy spreading of the Zeeman levels is different for each orientation (see Fig. 1.16), and therefore the value of (Sz) will be orientation dependent and (2) the values of (5, A/s Sz S, Ms) of Eq. (1.31) are orientation dependent as the result of efficient spin-orbit coupling. On the contrary, the contact coupling constant A is a constant whose value does not depend on the molecular orientation. 

We note here that Eq. (2.8) holds for a single electron in an orbital which is well separated by any other excited level. In the case of multiple unpaired electrons in different molecular orbitals, Eq. (2.8) still may hold in the absence of strong spin-orbit coupling effects but the interpretation of the hyperfine constant becomes complicated the hyperfine coupling is the sum of that for each molecular orbital. Indeed, each metal orbital which contains an unpaired electron is involved in a molecular orbital and provides a contribution to the total p for the various nuclei. The experimental data, however, provides through Eq. (2.8) the sum of the A values and therefore the sum of p. In order to make the spin density or contact constants comparable for different systems independent of the value of 5, i.e. independent of the number of electrons, the value of p is normalized to one electron, i.e. it is divided by the number of electrons which is just 2S (in such a way that p, /2S =1). Eq. (2.2) becomes... 

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